二期星·日十月三年〇七九一曆公年九十五國民華中育教僑華
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LEO英文中學會考試題預習專欄
報日僑華
"Using a =
in the sun for a terms.
1: term - 2 - L
it in sean
that the firat
Using n
2, the sum of the first two terma 8 - 2-6, therefore the second term 18 5.
Using a 3, the sum of the first three terme
• 15-6 18-3-15, therefore the third ters
Replacing n by {ns () the sum of the first i) terma 18-
~ (n-1).
2
2n-4n+2-nå
2n
nth term Bum of farat terme
ter:
中文中學會考
會考試題預習專欄
中國歷史科
(十九)
魯一民。
中國歷史科預習題答案 (十九) (五)隋唐(公元589年一一公元907年,
(十九)旗光題
1(A)天棗十四年(公元755年) 2.(A)樱神身帶
(B) TETA
(B)胸
(B)两晚法
堅道英文書院主編
The
5.9.
數學科
(十九)
san a.P. of common difference
MATHEMATICS (19)
Arithmetical Progression an arithmetical progressiON (A.P, )s. A series of terms that increases by a
conatant amount which may be positive or negativs.
The constant amount is known as the common difference
of the series and is usually denoted by 'd'.
To ascertain if a given series be an A.P. 1 18 necessary to subtract from each ters (except the first) the preceding term. If the results in all casas ba the same, the given series will be an A.P whose common difference is this common result.
To find e formula for the nth term of an A.P.. inosa common difference in 'd' and whose first term is 'ok
First term - a
Second teria
Third term wat
2d
a+ +
a + (1-1)a (21)d (3-1)日
From these results it can be seen that the nth. tera is at (n + 1)d.
The arithmetic mean (A.M.)" between two quantities and 'b' is that quantity which, when inserted between
forms with the three successive (a and b↑
terms of an A.P...
To find the arithmetic mean (A.K.) between Lat and
Get £ be the required A.K.Then,
DW211 three suggeüelva:terma of an A.P. The common : difference of the A.P. 18 (1- a) and (b
To find ca intari tanëtic means between 'a' and
Let a be the common difference of the A,P, formed. Then a 18 the (n 2)ta term of the 4.P.
Da
aced arithmetic means are a
#zero" a
ro ring the Bum 5 of n terms of at A.P term as 'a and whose common difference
whose first in
The last term of the series will be
* a+(a+d) + (a+2a)
Reversing the series
• ́ar(n=1)d] • [a+(n−2}d]
(2) gives
f2a+(n-1)d] • [2u+(n-k)d}
to a teras
n [2a + (n − 1)d]
MIza (n − 1)a]
Using (for the last term fa
can be written.
Dal
the
(which: 14
CA)
BA(6)
Example 4 The sun or five numbers in air. 1a 25 and the sum of their squares 18 165. Pind the numbers,
Let the middle term be
and the common
difference of the series bed then the terme are (a = 24), (a
2dj
1.0 Sa = 25
Expanding
substitution
10d
365
Hence the series 10 A
The Geometrical Progression The geometrical progression (G.P.) is a series of terme that increase or decrease in a constant ratio. This constant ratio is known as the common ratio of ins series and is usually denoted by
To find the nth term of a G.P. whose common ratio
and first term
Firat te zi
Second tera - Third term
From these it can-De seen that the ath. term
The geometric mean (0.M.) between two quantities Band b 18 that quantity which, when inserted between a and b, forma with then three successiva terms of a G.P.
To find the geometric mean between a and b
Let be the required C.M. Then, A
three successive terms of a G. P. The common ratio or
the GP, will be a and also b
To find the sun of the Tirar: common ratio 18 r and first term a
WDOBB
60 the required eum.
Therefore as a →→→→ ∞
the second term becomes negligible, whi when: r > 1 and S is then infinite
Thús when e Ci
and
答:(一)然后之點:
2. (B)
(D)
(B)朱湿(全)
然后及高宗皇后,各期天,害並列交永人,自命名零,太宗時入前周老人。太宗 能,人氣業告國感。並宗考位不久,因王皇后鬼你妈要寫,還再引入宮,叫真。武府 然人神蝶,有范眸,戴得高宗確信,5年后。高宗晚年風波病,不能上手,天小树 政考保武后所把持,從此武后期自成,大燮思宗宗及忠臣。中宗立,包含武后獎,另立 甘樂宗,不久,又度溫宗,银白铜查,號稱皇寺(天皇帝),是中國联史上第一位 女皇帝。黄后在位期間,私锦共空,但爲政斌有才。後儒宰相張柬之及胡臣数显等其
·臥病發動政變,淘武后退位,中宗 唐销始得恢復,武后之饿始寫..
(二)堂后之物
·农层台中宗之后,武后帝期間,中宗及后均被幽禁,中宗後帶封,常形性欲白殺 2.無資紥后所動。後來中宗復位,大小胡政淫龍筒求语。牶後政治須有心,當她禮 館之後,用武三卷勾箱,既殺大臣東乏,親子破伦,並發中宗,短少焿。以基
·太后身份理胡政,任用世宗室,白显大權泽落在空后手上。後信李隆基及太平公主所 殺容宗始得獲做,后之三此始思
(十二)试述唐代「安史之乱」之經過刀影响。(一九六九年會考試題)
答:(一)安史之亂之網碼
安祿山,史思明智營州姓品,紅茶集澍州电供長守理部。南山笃人狡詐,媒得玄 *宗數心,不要問,擢為河來,平療、范陽三親節度使。還至楊國忠零祖,與祿山不和,
群山裹已不利,速於天钱十四年(公元七五五年),以討楊國忠爲名,於范關舉兵。不 久,攻下浴陽、深關,李安相關陷落,山府,國。此時玄宗有與奔,太午夺 李雪位鵝嗽,改罕然是编宗、宗登位,卽詔令各方開。至德二年(公元七五七年 3、祿山為其子應將試。後來間又传满山部史思明所殺。原來當安群山填兵领店時,史 思明凉验其反,後期干等復两明我必張;於是又降街,關宗封他為己義王領 節變換。但不久思明城市與廢精勾結,透相呼喉,及思朗慶括後,乃吋糌大熊集帝 *此時患明復鐵法器,無官隶制拆*經經保亂。至公元七六三年,始偽郭子儀、李光郵及 电影兵所平
(=)
1. 形成之局:當安史之亂時,政府爲謀求早日平亂,乃安推谷將功臣,德茔亂帶後
> 他們多出任經説,形成日欲之禍,促使唐之表亡点 2.民生日因:地方等號,但麼利以來之能量,感受發現,國計民生因而日因。
3.外碳饭带入包:但缺等于假之功,更無書。陳旺者、南詔莱盛叛,入西北國防
(三)試述密代「細」形成之因及其时麼單之影的。
名:( 新鑭之稱的形成
由於安史之偏帶錢,各購親擁兵自重——唐初已有使之数,及至安史之亂後各觀
會時期第大1號數劑之軍政,財政之天欄。日久,但擁兵自帶,儼然
2.由於各额限偿多號條將一份安史之亂時,政府需求早日平亂,乃獎勵賊鋒號。但平後 各單將多出任信業節關鍵。如侯希逸爲渐洲强度伸;戴案爲准西線節使;田承嗣露 種關節度。其中尤以噬髋、成得、體博三冏罵害最烈,彼此互相聲,不供賦稅,目 無中央,胡英亦無可奈何。
(二)莊總寫之骱向
1.浙鐵關,使朝廷雜於對付,故不得不端防以兵。
2.在滿嫩下之地方經濟破,文化低落,我日後外族乘之入侵
3.不僅影响唐之裝亡,而且促成五代十國之局
(四)試謝明密室妄亡之原因:
答:盧自李洲開國,至製帝為未盡(忠),居,共有天下二百九十年(公元六一
八年——公元九〇七年)。究其身亡之因,有下列各點:
1.藩椒之,供地方形成割之局,安史之亂,雖然被平定了,但留下一個大洲戲,就是 裴鎮之稿。當時,政府為求早日平定內亂,多为玩勵民降將和平亂之功臣•故亂 平定後,他們多出為地方高官,因而形成親為術之為面。
2.宦官專機,使的政混亂您宫玄宗龜信高力士及宗任李韓國欲宦官逐漸得*
·因而專帶起來遠至案家以後,專浙英宗、文宗、武宗、宬實宗、秦宗、僖宗、昭宗 各帝均由宦官所獎文,使唐中葉以後,政權並入宦官之手。
3.胆黨之争,使國家人才霈————唐中絮以後,有肚,半為爭」,牛数以牛僧孺篇質
李業則以李家閔為首。乃由於政嵬不同而起,彼此意氣用事,互相排斥貶品,歷四十年南 不怠,國家人才因而被摧殘殊靈。
3.民變壞發,加速街亡——應亞然宗、偡宗年間,由於明政目宓內亂頻仍,加上天游流 ,於是民便叫紀,計有密南、王仙芝、黃立起來作亂。其中尤以西堡之亂含疫苗,凡氝 年,杄全園,後雖為朱全中所滅,但王家已表敗不堪,不久店家爲朱全忠服務
(五)玩宄题
中國歷史科預習問題:
(五)踏唐(公元589年——公元907年)
1. 唐太宗全高宗年間,中國有一位高僧往天堂求取佛密第一位(A);第二位是(B)
2.辛奘同國後,寫了一本西行遊記的帶,名叫(A),爲日從研究西域吏不可少的參考资
3.唐代提倡從古交運者,以(A)和(B)成就偉,後世球其文爲(C)•
武帝誅殺門,北周武帝抑禁保護二致,唐武宗減佛法,佛密靜此三次的铸
(B)
ELL, CA).
ly
geometric means between 21
Find the number
DE TAS. COSSon fatio of the G.P. Corned.
10 the fifta term of Mine:0.P.
Example 1 The sum or an A. 18 20, the first larm being 8 and the common difference":
of terms in the series.
Let n be the number or terms
Veing the formula
- [2a
1ja]
20 – in [16 + 2(n 1)]
n(ə
1). 9n
4) (n
5)
4 or 5
Example 2
Find the number or terms in an air. first term is 5.common difference 3, and Bum 55.
Lat n be the Teguated gumber of terms.
nose
Therefore required geometric meaz
3. CAD)
4. (A):
(B)
1.「會昌波法」是發生於:
(A)武宗之信
(C)高宗之時.
(B)太宗之時 (D)继宗之版
2. 將老子的道德經關成梵文傳往印度的高儈筒
(A)藏淨
(C)注額
(P)类
3.盧高宗時,有何面險往天竺求佛經:
(A)樂
(C)発有飯
4.唐代詩人,有所謂淇缲证,此滤以下列何人爲首
(A)陶
(C)李白
(B)主雕、
(1)李海菜
按案:
Example 6. In a geometridal progressLOR GHO TITRU term in 7, the last torm 448, and the sum 889. Fina the common ratio.
Deleter be the common TET10, a sne aumper or teras aza S the ass of a terNO..
089-1-
《廿七)試述佛教在唐傳播之大略悟形?艾在武宗時向以有「自自滅法!!. (廿八)試略浙文琪之生平及其對你學之實嗽。
(十九)唐代古文及特之發胺如何?其對後世之影响叉如何9.
更正上期錯誤的“
(十八)路(二)之第二行,第三句「遠」字誤掀篇「選」字, (十九)翘4-第二句未停至慈帝,根爲略宜帶、 (二十)翾4-末句瀨「事」字
** [10 + 3(n
小
1107a
3m2
22) (n
-5)
But in mua DS a positive integer
Sxample 3 The sum of the first a terms of a serios
18 2n a. Find the ath term and show that the series 18 an A.P.
4.25
Uning (2) sm(1) 689
889
#
8891
882 - 441*
2
(2)
Example 1 Fino vas sum or thu firms six terms or
the geometria series, whose third teza 10 27 and whose asith term 10. 8.
Let r be the common ravio OT, TRG Saries and: ine first vora.
(2),
243
THE SUM OF sza first mix terme
243
saan seri08).
(2/3)
665